Polynomial Jeopardy

Factoring Polynomials

100

Factor the polynomial:

x³+7x²+10x

x(x+5)(x+2)

200

Factor the polynomial:

9x³+6x²-3x

3x(3x-1)(x+1)

300

Factor the polynomial and find the zeros:

3x³+12x²-3x=12

x=-4,-1,1

400

Factor the polynomial to find the zeros. You may need to use the quadratic equation.

12x³=60x²+75x

x=0, (5 +/- 5sqrt2) /2

500

Factor the polynomial to find the zeros. 

x³+1=x²+x

x=-1,1

Synthetic Division

100

Use Synthetic Division to divide the following equation:

(x²-3x-40)/ (x+5)

x-8

200

Use Synthetic Division to solve the following equation:

(x³+3x²-x+2)/(x-1)

x²+4x+3, R:5

300

Use Synthetic Division to solve the following equation:

(x³+27) / (x+3)

x²-3x+9

400

Use Synthetic Division to solve the following equation:

(x⁴+3x³+x+4) / (x+3)

x³-3x²+12x-35, R:109

500

Use Synthetic Division to solve the following equation:

(x⁵+1) / (x+1)

x⁴-x³+x²-x+1

Long Division

100

Divide the polynomial by long division.

(3x²+7x-20) / (x+4)

3x-5

200

Use Long Division to solve the following equation:

2x³-3x²-18x-8) / (x-4)

2x²+5x+2

300

Use Long Division to solve the following equation:

(x²-7x+10)/ (x+3)

x-10, R:40

400

Use Long Division to solve the following equation:

(x³+5x²-3x-1) / (x-1)

x²+6x+3, R:2

500

Use Long Division to solve the following equation:

(2x²+x-7) / (x-5)

2x+11, R:48

Complex Numbers

100

Simplify

sqrt(-400)

20,-20

200

Add/Subtract

(4-5i)-(2-3i)

2-2i

300

multiply

(3+2i)(-3+4i)

-17+6i

400

Divide

(3+2i)/(4-3i)

(6+17i)/25

500

Solve the polynomial: (you will get a complex number solution)

x³+x²+x+1=0

x=-1,+/-i

Random

100

Find all zeroes. 

f(x) = x(x+3)(2x - 4)²

x = 0 

x = -3 

x = 2 mult. of 2

200

Is (x-2) a factor of 2x² -20x + 67?

No, it has a remainder

300

Is (2x+7) a factor of 2x³ + 5x² - 19x -42 ?

Yes, no remainder left over

400

Is (x-1) a factor of x³ + 4x² -16x + 8

No, there is a remainder

500

Is (x-1) a factor of (x³ + 2x - 3) ?

yes! If you divide, it has remainder 0